Hide and seek on complex networks

Signaling pathways and networks determine the ability to communicate in systems ranging from living cells to human society. We investigate how the network structure constrains communication in social-, man-made and biological networks. We find that human networks of governance and collaboration are predictable on teat-a-teat level, reflecting well defined pathways, but globally inefficient. In contrast, the Internet tends to have better overall communication abilities, more alternative pathways, and is therefore more robust. Between these extremes the molecular network of Saccharomyces cerevisea is more similar to the simpler social systems, whereas the pattern of interactions in the more complex Drosophilia melanogaster, resembles the robust Internet.Comment: 5 pages, 5 figure

Simple observations concerning black holes and probability

It is argued that black holes and the limit distributions of probability theory share several properties when their entropy and information content are compared. In particular the no-hair theorem, the entropy maximization and holographic bound, and the quantization of entropy of black holes have their respective analogues for stable limit distributions. This observation suggests that the central limit theorem can play a fundamental role in black hole statistical mechanics and in a possibly emergent nature of gravity.Comment: 6 pages Latex, final version. Essay awarded "Honorable Mention" in the Gravity Research Foundation 2009 Essay Competitio

High-pressure synthesis of rock salt LiMeO2-ZnO (Me = Fe3+, Ti3+) solid solutions

Metastable LiMeO2-ZnO (Me = Fe3+, Ti3+) solid solutions with rock salt crystal structure have been synthesized by solid state reaction of ZnO with LiMeO2 complex oxides at 7.7 GPa and 1350-1450 K. Structure, phase composition, thermal stability and thermal expansion of the recovered samples have been studied by X-ray diffraction with synchrotron radiation. At ambient pressure rock salt LiMeO2-ZnO solid solutions are kinetically stable up to 670-800 K depending on the composition.Comment: 11 pages, 3 figures, 1 tabl

A Classical Bound on Quantum Entropy

A classical upper bound for quantum entropy is identified and illustrated, $0\leq S_q \leq \ln (e \sigma^2 / 2\hbar)$, involving the variance $\sigma^2$ in phase space of the classical limit distribution of a given system. A fortiori, this further bounds the corresponding information-theoretical generalizations of the quantum entropy proposed by Renyi.Comment: Latex2e, 7 pages, publication versio

Heat transport in Bi_{2+x}Sr_{2-x}CuO_{6+\delta}: departure from the Wiedemann-Franz law in the vicinity of the metal-insulator transition

We present a study of heat transport in the cuprate superconductor Bi_{2+x}Sr_{2-x}CuO_{6+\delta} at subkelvin temperatures and in magnetic fields as high as 25T. In several samples with different doping levels close to optimal, the linear-temperature term of thermal conductivity was measured both at zero-field and in presence of a magnetic field strong enough to quench superconductivity. The zero-field data yields a superconducting gap of reasonable magnitude displaying a doping dependence similar to the one reported in other families of cuprate. The normal-state data together with the results of the resistivity measurements allows us to test the Wiedemann-Franz(WF) law, the validity of which was confirmed in an overdoped sample in agreement with previous studies. In contrast, a systematic deviation from the WF law was resolved for samples displaying either a lower doping content or a higher disorder. Thus, in the vicinity of the metal-insulator cross-over, heat conduction in the zero-temperature limit appears to become significantly larger than predicted by the WF law. Possible origins of this observation are discussed.Comment: 9 pages including 7 figures, submitted to Phys. Rev.

A typical reconstruction limit of compressed sensing based on Lp-norm minimization

We consider the problem of reconstructing an $N$-dimensional continuous vector \bx from $P$ constraints which are generated by its linear transformation under the assumption that the number of non-zero elements of \bx is typically limited to $\rho N$ ($0\le \rho \le 1$). Problems of this type can be solved by minimizing a cost function with respect to the $L_p$-norm ||\bx||_p=\lim_{\epsilon \to +0}\sum_{i=1}^N |x_i|^{p+\epsilon}, subject to the constraints under an appropriate condition. For several $p$, we assess a typical case limit $\alpha_c(\rho)$, which represents a critical relation between $\alpha=P/N$ and $\rho$ for successfully reconstructing the original vector by minimization for typical situations in the limit $N,P \to \infty$ with keeping $\alpha$ finite, utilizing the replica method. For $p=1$, $\alpha_c(\rho)$ is considerably smaller than its worst case counterpart, which has been rigorously derived by existing literature of information theory.Comment: 12 pages, 2 figure

H-theorem for classical matter around a black hole

We propose a classical solution for the kinetic description of matter falling into a black hole, which permits to evaluate both the kinetic entropy and the entropy production rate of classical infalling matter at the event horizon. The formulation is based on a relativistic kinetic description for classical particles in the presence of an event horizon. An H-theorem is established which holds for arbitrary models of black holes and is valid also in the presence of contracting event horizons

The elusive source of quantum effectiveness

We discuss two qualities of quantum systems: various correlations existing between their subsystems and the distingushability of different quantum states. This is then applied to analysing quantum information processing. While quantum correlations, or entanglement, are clearly of paramount importance for efficient pure state manipulations, mixed states present a much richer arena and reveal a more subtle interplay between correlations and distinguishability. The current work explores a number of issues related with identifying the important ingredients needed for quantum information processing. We discuss the Deutsch-Jozsa algorithm, the Shor algorithm, the Grover algorithm and the power of a single qubit class of algorithms. One section is dedicated to cluster states where entanglement is crucial, but its precise role is highly counter-intuitive. Here we see that distinguishability becomes a more useful concept.Comment: 8 pages, no figure

Exploring the randomness of Directed Acyclic Networks

The feed-forward relationship naturally observed in time-dependent processes and in a diverse number of real systems -such as some food-webs and electronic and neural wiring- can be described in terms of so-called directed acyclic graphs (DAGs). An important ingredient of the analysis of such networks is a proper comparison of their observed architecture against an ensemble of randomized graphs, thereby quantifying the {\em randomness} of the real systems with respect to suitable null models. This approximation is particularly relevant when the finite size and/or large connectivity of real systems make inadequate a comparison with the predictions obtained from the so-called {\em configuration model}. In this paper we analyze four methods of DAG randomization as defined by the desired combination of topological invariants (directed and undirected degree sequence and component distributions) aimed to be preserved. A highly ordered DAG, called \textit{snake}-graph and a Erd\:os-R\'enyi DAG were used to validate the performance of the algorithms. Finally, three real case studies, namely, the \textit{C. elegans} cell lineage network, a PhD student-advisor network and the Milgram's citation network were analyzed using each randomization method. Results show how the interpretation of degree-degree relations in DAGs respect to their randomized ensembles depend on the topological invariants imposed. In general, real DAGs provide disordered values, lower than the expected by chance when the directedness of the links is not preserved in the randomization process. Conversely, if the direction of the links is conserved throughout the randomization process, disorder indicators are close to the obtained from the null-model ensemble, although some deviations are observed.Comment: 13 pages, 5 figures and 5 table